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Search: id:A128288
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| 3, 13, 37, 43, 53, 67, 83, 107, 157, 163, 173, 197, 227, 277, 283, 293, 307, 317, 347, 373, 397, 443, 467, 523, 547, 557, 563, 587, 613, 643, 653, 677, 683, 733, 757, 773, 787, 797, 827, 853, 877, 883, 907, 947, 997, 1013, 1093, 1117, 1123, 1163, 1187, 1213
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OFFSET
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2,1
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COMMENT
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3 divides A023163(n) for n>1. A023163(n) are the numbers n such that Fib(n) == -2 (mod n). Almost all terms of a(n) are prime that belong to A003631 = {2, 3, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97} Primes congruent to {2, 3} mod 5; that are also the primes p that divide Fibonacci(p+1). The first composite term is a(74) = 1853 = 17*109. The second composite term is 9701 = 89*109. The third composite term is 10877 = 73*149 belong to A069107(n) Composite n such that n divides F(n+1) where F(k) are the Fibonacci numbers. Composite terms in a(n) are listed in A128289 = {1853, 9701, 10877, 17261, ...}.
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FORMULA
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a(n) = A023163(n)/3 for n>1.
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EXAMPLE
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A023163(n) begins {1, 9, 39, 111, 129, 159, 201, 249, 321, 471, 489, 519, ...}.
Thus a(2) = A023163(2)/3 = 9/3 = 3, a(3) = A023163(3)/3 = 39/3 = 13.
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CROSSREFS
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Cf. A002708, A023172, A023173, A023162, A023163 = numbers n such that Fib(n) == -2 (mod n). Cf. A003631, A069107, A128289 = Composite terms in A128288.
Sequence in context: A058214 A108480 A061483 this_sequence A113115 A107136 A098547
Adjacent sequences: A128285 A128286 A128287 this_sequence A128289 A128290 A128291
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 24 2007
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